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The fluid flow through porous media. Regularity of the free surface

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Abstract

The fluid flow through an earth dam separating two water reservoirs of different levels gives rise to a free boundary problem. In [1] we have proved the existence of a solution to this problem. In this paper we show that the free boundary is regular.

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References

  1. ALT, H.W.: A Free Boundary Problem Associated with the Flow of Ground water. Arch. Rat. Mech. Anal, (to appear)

  2. BREZIS, H.R.: Problèmes unilateraux. J. Math. Pur. Appl.51, 1–168 (1972)

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  3. BREZIS, H.R., STAMPACCHIA, G.: Sur la régularité de la solution d'inéquations elliptiques. Bull. Soc. Math. France96, 153–180 (1968)

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  4. CAFFARELLI, L.A.: The regularity of free boundaries in higher dimensions, (to appear)

  5. KINDERLEHRER, D.,NIRENBERG, L.: Regularity in Free Boundary Problems. (to appear)

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  1. Institut für Angewandte Mathematik der Universität, Im Neuenheimer Feld 294, 6900, Heidelberg, Bundesrepublik Deutschland

    Hans Wilhelm Alt

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  1. Hans Wilhelm Alt
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Alt, H.W. The fluid flow through porous media. Regularity of the free surface. Manuscripta Math 21, 255–272 (1977). https://doi.org/10.1007/BF01167879

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  • DOI: https://doi.org/10.1007/BF01167879

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